# How do the actual profiles compare to the theoretical prediction of the Grossman model?

2. In the Grossman model, the main reason that wages increase the ROR is that they multiply the time-savings of becoming healthier. Let’s think about what this implies for wage differences in health. a. Simulate a Grossman model with the following set up: i. A high wage of \$20 and a low wage of \$10, and a price of medical inputs equal to \$200. ii. Interest rate of 0.05 iii. Depreciation rate of 0.1 iv. No change in Tr,. v. ut = 10/nHt + 1n13, vi. Tt* = 24 (1 — vii. nt = x(a’ + (1 —pl-‘)e-TY with a = 0.5 and a = 0.2 Calculate optimal health stock and the amount of healthy time for a low wage person for many different values of x between 5 and 1. The first case imposes a “low health world”, where the investment price is high and health stock is low. The second case imposes a “high health world”, where investment is cheap and health is high.
Make one graph of 77 against x with lines for the high and low wage people. Does the Grossman model predict a larger difference in healthy time between high and low wage people when investment is costly (and health is low) or when investment is cheap (and health is high)?
b. Now let’s see if this is actually true. Use ps 3 . dt a again and calculate real income, and the two dummies (no bed days and excellent/very good/good health). i. Summarize your real income variable (using the option: , de t a i 1) and make a dummy called h i gh i n c that equals one for respondents with income above the median. ii. Collapse your data to means of the bed days and health variable by year and h i gh i n c. Do a reshape (wide) to make your dataset have observations defined by year and separate variables for low and high income averages. Make variables that equal the high/low difference i n t he health and disability variables. iii. Plot the health averages over time with lines for the low and high income people. Was health improving over this time? (Note that health is only asked after 1972.) Does this fit with the Grossman model? iv. Plot of the difference in health between high and low income people over time. Was self-reported health converging between the two groups? Does this fit with the Grossman model? v. Plot the difference in health time (the average of the “no disability days” variable) between high and low income people over time. Was the amount of healthy time converging between the two groups? Does this fit with the Grossman model?
1. The Grossman model implies that higher wage people are in better health, but it also has some pretty strong implications for how that relationship should be shaped. a. Simulate a Grossman modelia. 1- • .1 T with the following set up: i. Interest rate of 0.05 ii. Depreciation rate of 0.1 iii. No change in re. iv. lit = 101n1-1, + Ink v. Tt* = 24 (1 — vi. ift = (a’tvi-a + (1 — a)apl-a)1 with a = 0.5 and a = 0.2 Calculate optimal health stock and the amount of healthy time for people whose wage is 1, 2, 3, 4, …, all the way up to 50. Make one plot of the health stock versus the wage and another of healthy time versus the wage.
How is this relationship shaped? What pieces of the Grossman model equation make this true?
b. lispv let’s see if this is actually true. The NHIS extract ps 3 . dta a contains information on disability bed days in the last two weeks (T — Tt*), and total family income (a bad measure of w) from 1963 through 1996 for employed adults ages 25-64.2 Use the dofile ¦ n¦ ¦ 1 ¦ 1 called income_recode_ps3. do, to recode the values (to the midpoint of each bin) and also to adjust them to 2000 dollars (using a command called cpigen that automatically brings in values of the Consumer Price Index).3 Use the egen subcommand cut, to make bins of your income variable that are 2000 wide: egen inccat = cut (inc) , at (0 (2000)80000 100000) c. Now make a dummy that equals one for people in excellent, very good, or good health (we did something similar in lab notes 2), and another that equals one for respondents who had no disability days in the last two weeks (make sure to check out the meaning of “niu” in the 60s). Collapse the dataset so that it has the average of these two dummies by values of inccat. d. Make scatter plots of each variable against income. How do the actual profiles compare to the theoretical prediction of the Grossman model?
Hint: use a forval loop! Think about how you’ll store your answer (the values of H and T•) each time. 2 1967 is omitted because they asked their disability bed days question to a weird subsample of respondents. 3 The values of cpi that are added equal the ratio of each year’s CPI to the 2000 CPI. If income is in current dollars, and you want to express it in constant 2000 dollars, should you multiply or divide inc by cpi = CPIYYYY/CPI2000?